In order to analyze the pricing of portfolio credit risk – as revealed by tranche spreads of a popular credit default swap (CDS) index – we extract risk-neutral probabilities of default (PDs) and physical asset return correlations from single-name CDS spreads. The time profile and overall level of index spreads validate our PD measures. At the same time, the physical asset return correlations are too low to account for the spreads of index tranches and, thus, point to a large correlation risk premium. This premium, which covaries negatively with current realized correlations and positively with future realized correlations, sheds light on market perceptions of and attitude towards correlation risk.